A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation
zbMATH Open document ID: 1480.35363
author: Rui-Qi Wang
author: Delu Zeng
author: Liming Ling
author: Bao-Feng Feng
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2021-07-09T00:00:00Z
review text: Modulation instability (MI) is a pervasive phenomenon in nonlinear science. It is inevitable for simulating rogue wave or breather solutions of the focusing nonlinear Schrödinger equation (NLSE) and other application problems with MI involved. Due to MI, the small perturbation on the boundary can lead to large and non-negligible errors for the simulation of initial-boundary problems. To deal with this challenging problem, the authors propose a method to modify the boundary problem through a deep learning algorithm so that the long time simulation for the rogue wave or breather solutions to the NLSE can be performed with a superior numerical errors. This method paves a way to simulate other physical problems with MI.
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q41
Mathematics Subject Classification ID: 76B25
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 68Q32
Mathematics Subject Classification ID: 68T07
Mathematics Subject Classification ID: 35C08
zbMATH DE Number: 7370464
zbMATH Keywords: deep learning
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: rogue wave
zbMATH Keywords: breather
zbMATH Keywords: numerical simulation
reviewed by: Jiqiang Zheng
describes a project that uses: DGM
describes a project that uses: Adam
MaRDI profile type: Publication
full work available at URL: j.cnsns.2021.105896
OpenAlex ID: W3164864419
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DOI: 10.1016/J.CNSNS.2021.105896
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description: scientific article; zbMATH DE number 7370464